DEPENDENCE OF STRESS ESTIMATES 

 ON C D 



A constant drag coefficient was used to compute the 

 surface wind stress data displayed in Appendix I. Stress 

 calculations were made for each wind report and then 

 averaged to form the resultant monthly mean vectors. 

 Different results might have been obtained if the stress 

 were calculated from monthly mean wind data, or if ef- 

 fects of atmospheric stability were considered. These as- 

 pects are discussed below. 



Errors associated with the observational data used in 

 this study place certain limitations on the form of the 

 bulk exchange formula expressed in Equation (1). If 

 measurement errors are large, there may be little value in 

 refining the parameterization by replacing C n by a 

 variable drag coefficient which is a function of stability 

 or wind speed. Even with a constant C n , the bulk for- 

 mula contains nonlinearities. Therefore, the drag coef- 

 ficient must be appropriate for the particular time- 

 averaged winds used in the calculations. That is, a drag 

 coefficient appropriate for synoptic wind observations 

 would not be appropriate for winds averaged over a 

 month. 



Effects of Averaging 



The empirically derived transfer coefficient Co , deter- 

 mined by eddy correlation and profile methods, is based 

 on wind measurements averaged over periods of 30 to 60 

 min. Pond (1975) indicated that the appropriate values 

 of I W in I , £/ 10 , and V 10 should be obtained over a period 

 of a few minutes to a few hours at most. If the surface 

 stress were calculated using winds averaged over much 

 longer periods, a higher drag coefficient would be re- 

 quired. The surface stress calculated from a monthly 

 mean surface wind field will be significantly less than the 

 surface stress field calculated as the mean of the in- 

 dividual stress estimates, if the same drag coefficient is 

 used and all other parameters are held constant. 



The difference described above has been determined 

 for the data used in this study. For each 1-degree square 

 area and long-term month, the following ratio has been 

 calculated: 



(C D ) 



=m/[ 



[p„(K 



(4) 



where! T lis the magnitude of the monthly mean surface 

 stress, | W 10 | is the magnitude of the monthly mean sur- 

 face wind, and (Co ) equ is an equivalent drag coefficient. 

 This is the value which would be necessary to make the 

 stress values calculated from the monthly mean wind 

 data agree with the values calculated as the means of in- 

 dividual stress estimates. 



Values of (C D ) equ for the months of June and Decem- 

 ber are shown in Figures 3 and 4. The values are sig- 

 nificantly different from the constant value of 

 C D = 0.0013 employed in this study. In all cases, 

 (C D ) equ is greater than C D . Spatial and seasonal 



variability is marked. There is a tendency for much 

 higher values in the northern section of the grid than in 

 the southern area. Large values of (C D ) equ are more evi- 

 dent in December than in June. Geographical and 

 seasonal variations in the quantity (Co ) equ agree with 

 the general geographical and seasonal fluctuations in 

 meteorological conditions over the northeast Pacific 

 Ocean. This would indicate that a large part of the 

 monthly variance of the wind stress data is due to actual 

 intramonth fluctuations and not due to observational 

 errors. If a resultant surface wind stress were calculated 

 from the monthly mean wind field, these calculations 

 imply that the wind stress estimates would be under- 

 estimated, on average, by as much as 50% to 100%. The 

 departures would be even larger off Oregon and Washing- 

 ton. 



Effect of Atmospheric Stability 



Investigations on the functional form of the drag coef- 

 ficient have alternately suggested constant values, or a 

 dependence on wind speed. Wilson (1960) gave a detailed 

 review of the available data and adopted values of 

 C D = 0.0024 ± 0.005 for strong winds and C D = 0.0015 

 ± 0.0008 for light winds. Smith (1970) proposed a con- 

 stant value of C D = (1.35 ± 0.34)_X 10" 3 . Wu (1969) 

 adopted the form C D = (0.5 X £/ 10 '') x 10~ 3 - Con- 

 sidering the large scatter in the open ocean deter- 

 minations of Co , the lack of conclusive data at wind 

 speeds greater than 15 ms" 1 , and the lack of agreement 

 among individual observers, a constant value for the 

 neutral drag coefficient was used in this study. 



Recent investigations by Davidson (1974) and Den- 

 man and Miyake (1973) have demonstrated the depen- 

 dence of the drag coefficient on atmospheric stability and 

 the spectral shape of the ocean wave field. A generally 

 accepted formulation of the dependence of C D on wave 

 properties does not seem well enough established to be 

 incorporated in the calculations of surface wind stress 

 based on historical ship observations. However, effects of 

 atmospheric stability on the momentum exchange may 

 be significant in regions where seasonal upwelling 

 typically produces a stable boundary layer. 



The specific effects of atmospheric stability on the ex- 

 change of momentum have not been completely deter- 

 mined and are still under investigation. However, for a 

 given wind speed, the effect of stable (unstable) 

 stratification is to decrease (increase) the magnitude of 

 the momentum exchange (surface wind stress) across the 

 atmosphere-ocean interface. 



In order to investigate the effects of atmospheric 

 stability, the monthly mean fields of surface wind stress 

 were recomputed, replacing the constant value Co in 

 Equation (1) by a coefficient varying with atmospheric 

 stability. Deardorff (1968) defined the bulk Richardson 

 number as an appropriate dimensionless measure of at- 

 mospheric stability. Deardorff s method was adopted to 

 parameterize the dependence of the drag coefficient on 

 stability, while neutral stability was assumed when the 

 absolute value of the air-sea temperature difference was 



